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Two Norwegian youths who wrecked a 5,000-year-old rock carving of a figure on skis risk prosecution under Norway's Cultural Heritage Act, the archaeologist who surveyed the damage confirmed on Sunday.

The vandals said they had been trying to improve the historical site by carving over the outline of the figure to make it easier to see - but local officials described their makeshift restoration as a "tragedy" for Norway's cultural heritage.

Tor-Kristian Storvik, the county archaeologist for Norway's Nordland County, said that he was pleased the boys had come forward, but he was not prepared to retract the crime report sent to police.

BEFORE: How the prehistoric carving of a skier on the Island of Tro in Norway looked. Photo / Supplied

The carving on the island of Tro on Norway's west coast is one of Norway's most famous historical sites, providing some of the earliest evidence of skiing anywhere in the world. The carving inspired the symbols used for the Winter Olympics in Lillehammer in 1994.

Mr Storvik rushed to the site to survey the damage last week after someone with a holiday house on the island telephoned him to report that a sharp object had been used to deface the carvings.

"It's a sad, sad story," he said. "The new lines are both in and outside where the old marks had been. We will never again be able to experience these carvings again the way we have for the last 5,000 years."

As well as the skier, a carving of a whale which formed part of the same hunting scene, had also suffered serious damage, he said.

The two boys on Friday issued a public apology for the vandalism, which was put out as part of a press release by the local municipality.

"We have talked to the perpetrators and their families and they want to apologize for what they have done," Bård Anders Langø, the local mayor, said.

"It was done out of good intentions. They were trying to make it more visible actually, and I don't think they understood how serious it was."

The damage has sparked strong reactions on social media, with many calling for the pair, who remain anonymous, to face punishment.